Abstract: In formal concept analysis, the so-called "arrow relation" plays an important role in reducing the size of a for- mal context and recognizing a compatible subcontext of a formal context Thus,how to quick determine the arrow rela- lion between the objects and the attributes of a formal context is worth to be investigated. This study first gave an e- quivalent theorem of checking whether or not there is an arrow relationship between an object and an attribute of a for- mal context Then a ctuick algorithm of determining the arrow relation between the objects and the attributes of a formal context was developed. Finally, a real example and numerical experiments were used to demonstrate the feasibility and efficiency of the proposed algorithm.

Key words: Formal concept analysis, Formal context, Arrow relation, Quick algorithm